4/4x=3/x-2

Solution for 4/4x=3/x-2 equation:

4/4x=3/x-2

We move all terms to the left:

4/4x-(3/x-2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

4/4x-3/x+2=0

We calculate fractions


4x/4x^2+(-12x)/4x^2+2=0

We multiply all the terms by the denominator


4x+(-12x)+2*4x^2=0

Wy multiply elements

8x^2+4x+(-12x)=0

We get rid of parentheses

8x^2+4x-12x=0

We add all the numbers together, and all the variables

8x^2-8x=0

a = 8; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·8·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*8}=\frac{16}{16}
=1
$